The topic of equation
of a circle is a new topic introduced in the new syllabus 2008 of
Additional Mathematics. Hence, there are no past year exam
questions on this topic in the ten years series.
The equation of the circle was once set in the late 60s and early
70s.
If you need more practices, you can go to Bras Basah Complex second
hand bookshop to look for the old, old ten years series.
Question 1
The equation of a circle is x^2 + y^2 - 4x + 6y - 12 =0
Find the equation of the new circle, which is a reflection of the
circle
in the x-axis. (Hint : There is a short-cut to this question)
Question 2
(a) Show that the line 4y = x - 3 touches the circle
x^2 + y^2 - 4x - 8y + 3 = 0
(b) The straight line x = 3 intersects the circle
x^2 + y^2 - 8x - 10y - 9 = 0 at the points P and Q.
Find the equations of tangents at P and Q.
Another new topic is
the solving of an inequality with modulus introduced in the new
syllabus 2008 of Additional Mathematics. Hence, there are no past
year exam questions on this topic in the ten years series.
In the previous syllabus, students are required to sketch the
inequality and state the number of solutions but in the new
syllabus, students are required to solve an inequality with
modulus.
Question 1
Without using a graphics
calculator, solve (not sketch) the
inequality
l x^2 - 3x - 7 l < 3.
Another new topic
is partial fraction introduced in the new syllabus 2008 of
Additional Mathematics.
The topic of partial fraction was previously in the old syllabus of
"A" level Maths C. Hence, students will have to look for the old
ten years series of A" level Maths C to practise on the topic of
partial fraction.
Question
1
Express in partial
fraction
(17x^2 +23x + 12)/[(3x+4)(x^2+4)]
Another new topic is
the R-formula, addition and subtraction of angles, double angles
and factor formulae introduced in the new syllabus 2008 of
Additional Mathematics.
The topic of R-formula, addition and subtraction of angles, double
angles and factor formulae was previously set in the 80s and 90s.
If you need more practices, you can go to Bras Basah Complex second
hand bookshop to look for the old, old ten years series.
Question 1
Solve the equation 3cosx - 2sinx = 2 for all angles between 0
degree and 360 degrees inclusive.
Another new topic is
the midpoint theorem, intercept theorem, alternate segment or
tangent chord theorem, intersecting chords theorem and tangent
secant theorem introduced in the new syllabus 2008 of Additional
Mathematics.
The midpoint theorem, intercept theorem, alternate segment or
tangent chord theorem were previously in the old syllabus of E.
Maths. If you need more practices, you can go to Bras Basah Complex
second hand bookshop to look for the old, old ten years
series.
However, the intersecting chords theorem and tangent secant theorem
have never appeared before in the "O" and "A" level Maths exam
questions. (I have all the "A" level Maths C exam papers from 1968
to 2007, "O" level Add Maths (includes "AO" level Maths) and E.
Maths exam questions from 1958 to 2007, "N" level Maths exam
questions from first year 1984 to 2007) Hence, there will be no
past exam questions on this topic in the ten years series. If you
need more practices, you can only try practising on the question in
the specimen papers provided by MOE for the new syllabus 2008 of
additional mathematics.
Another new topic is
the use of a (alpha) and
b (beta) in the quadratic
equation introduced in the new syllabus 2008 of Additional
Mathematics.
The use of a (alpha) and
b (beta) in the quadratic
equation was once set in the late 70s and early 80s.If you need
more practices, you can go to Bras Basah Complex second hand
bookshop to look for the old, old ten years series.
Question 1
Given that one root of the equation
x^2 + px + q = 0
is twice the other, express q in terms of p.
Question 2
Form the quadratic equation for which the sum of the roots is 2 and
the sum of the squares of the roots is 18.
